Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(1549,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1549.3 | ||
Root | \(1.40680 + 0.144584i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.1549 |
Dual form | 1800.2.d.q.1549.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.144584 | − | 1.40680i | 0.102237 | − | 0.994760i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.95819 | − | 0.406803i | −0.979095 | − | 0.203402i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.62721i | − | 1.37096i | −0.728093 | − | 0.685479i | \(-0.759593\pi\) | ||
0.728093 | − | 0.685479i | \(-0.240407\pi\) | |||||||
\(8\) | −0.855416 | + | 2.69597i | −0.302435 | + | 0.953170i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 6.20555i | − | 1.87104i | −0.353269 | − | 0.935522i | \(-0.614930\pi\) | ||
0.353269 | − | 0.935522i | \(-0.385070\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.578337 | −0.160402 | −0.0802009 | − | 0.996779i | \(-0.525556\pi\) | ||||
−0.0802009 | + | 0.996779i | \(0.525556\pi\) | |||||||
\(14\) | −5.10278 | − | 0.524438i | −1.36377 | − | 0.140162i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.66902 | + | 1.59320i | 0.917256 | + | 0.398299i | ||||
\(17\) | − | 1.42166i | − | 0.344804i | −0.985027 | − | 0.172402i | \(-0.944847\pi\) | ||
0.985027 | − | 0.172402i | \(-0.0551528\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.62721i | 1.29097i | 0.763772 | + | 0.645486i | \(0.223345\pi\) | ||||
−0.763772 | + | 0.645486i | \(0.776655\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8.72999 | − | 0.897225i | −1.86124 | − | 0.191289i | ||||
\(23\) | − | 5.62721i | − | 1.17336i | −0.809821 | − | 0.586678i | \(-0.800436\pi\) | ||
0.809821 | − | 0.586678i | \(-0.199564\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.0836184 | + | 0.813607i | −0.0163989 | + | 0.159561i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.47556 | + | 7.10278i | −0.278855 | + | 1.34230i | ||||
\(29\) | 2.00000i | 0.371391i | 0.982607 | + | 0.185695i | \(0.0594537\pi\) | ||||
−0.982607 | + | 0.185695i | \(0.940546\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.57834 | −0.463083 | −0.231542 | − | 0.972825i | \(-0.574377\pi\) | ||||
−0.231542 | + | 0.972825i | \(0.574377\pi\) | |||||||
\(32\) | 2.77180 | − | 4.93124i | 0.489989 | − | 0.871729i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.00000 | − | 0.205550i | −0.342997 | − | 0.0352516i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.83276 | 1.28770 | 0.643849 | − | 0.765152i | \(-0.277336\pi\) | ||||
0.643849 | + | 0.765152i | \(0.277336\pi\) | |||||||
\(38\) | 7.91638 | + | 0.813607i | 1.28421 | + | 0.131984i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.25443 | −0.820603 | −0.410302 | − | 0.911950i | \(-0.634577\pi\) | ||||
−0.410302 | + | 0.911950i | \(0.634577\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.25443 | −1.10629 | −0.553145 | − | 0.833085i | \(-0.686572\pi\) | ||||
−0.553145 | + | 0.833085i | \(0.686572\pi\) | |||||||
\(44\) | −2.52444 | + | 12.1517i | −0.380573 | + | 1.83193i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −7.91638 | − | 0.813607i | −1.16721 | − | 0.119960i | ||||
\(47\) | − | 6.78389i | − | 0.989532i | −0.869026 | − | 0.494766i | \(-0.835254\pi\) | ||
0.869026 | − | 0.494766i | \(-0.164746\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.15667 | −0.879525 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.13249 | + | 0.235269i | 0.157049 | + | 0.0326260i | ||||
\(53\) | 2.00000 | 0.274721 | 0.137361 | − | 0.990521i | \(-0.456138\pi\) | ||||
0.137361 | + | 0.990521i | \(0.456138\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 9.77886 | + | 3.10278i | 1.30676 | + | 0.414626i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.81361 | + | 0.289169i | 0.369445 | + | 0.0379697i | ||||
\(59\) | − | 2.20555i | − | 0.287138i | −0.989640 | − | 0.143569i | \(-0.954142\pi\) | ||
0.989640 | − | 0.143569i | \(-0.0458579\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.4111i | 1.58908i | 0.607213 | + | 0.794539i | \(0.292288\pi\) | ||||
−0.607213 | + | 0.794539i | \(0.707712\pi\) | |||||||
\(62\) | −0.372787 | + | 3.62721i | −0.0473440 | + | 0.460657i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.53653 | − | 4.61235i | −0.817066 | − | 0.576544i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.00000 | −0.488678 | −0.244339 | − | 0.969690i | \(-0.578571\pi\) | ||||
−0.244339 | + | 0.969690i | \(0.578571\pi\) | |||||||
\(68\) | −0.578337 | + | 2.78389i | −0.0701337 | + | 0.337596i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.41110 | −0.998214 | −0.499107 | − | 0.866540i | \(-0.666339\pi\) | ||||
−0.499107 | + | 0.866540i | \(0.666339\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.00000i | 0.702247i | 0.936329 | + | 0.351123i | \(0.114200\pi\) | ||||
−0.936329 | + | 0.351123i | \(0.885800\pi\) | |||||||
\(74\) | 1.13249 | − | 11.0192i | 0.131650 | − | 1.28095i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 2.28917 | − | 11.0192i | 0.262586 | − | 1.26398i | ||||
\(77\) | −22.5089 | −2.56512 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.42166 | −0.609985 | −0.304992 | − | 0.952355i | \(-0.598654\pi\) | ||||
−0.304992 | + | 0.952355i | \(0.598654\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.759707 | + | 7.39194i | −0.0838956 | + | 0.816304i | ||||
\(83\) | −3.25443 | −0.357220 | −0.178610 | − | 0.983920i | \(-0.557160\pi\) | ||||
−0.178610 | + | 0.983920i | \(0.557160\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1.04888 | + | 10.2056i | −0.113103 | + | 1.10049i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 16.7300 | + | 5.30833i | 1.78342 | + | 0.565869i | ||||
\(89\) | −13.2544 | −1.40497 | −0.702483 | − | 0.711700i | \(-0.747925\pi\) | ||||
−0.702483 | + | 0.711700i | \(0.747925\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.09775i | 0.219904i | ||||||||
\(92\) | −2.28917 | + | 11.0192i | −0.238662 | + | 1.14883i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.54359 | − | 0.980843i | −0.984347 | − | 0.101166i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.84333i | 0.491765i | 0.969300 | + | 0.245883i | \(0.0790778\pi\) | ||||
−0.969300 | + | 0.245883i | \(0.920922\pi\) | |||||||
\(98\) | −0.890158 | + | 8.66123i | −0.0899196 | + | 0.874916i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.00000i | 0.199007i | 0.995037 | + | 0.0995037i | \(0.0317255\pi\) | ||||
−0.995037 | + | 0.0995037i | \(0.968274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 2.47054i | − | 0.243429i | −0.992565 | − | 0.121715i | \(-0.961161\pi\) | ||
0.992565 | − | 0.121715i | \(-0.0388393\pi\) | |||||||
\(104\) | 0.494719 | − | 1.55918i | 0.0485112 | − | 0.152890i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.289169 | − | 2.81361i | 0.0280865 | − | 0.273282i | ||||
\(107\) | 14.0978 | 1.36288 | 0.681441 | − | 0.731873i | \(-0.261354\pi\) | ||||
0.681441 | + | 0.731873i | \(0.261354\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 7.25443i | − | 0.694848i | −0.937708 | − | 0.347424i | \(-0.887056\pi\) | ||
0.937708 | − | 0.347424i | \(-0.112944\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.77886 | − | 13.3083i | 0.546051 | − | 1.25752i | ||||
\(113\) | − | 9.08719i | − | 0.854851i | −0.904051 | − | 0.427425i | \(-0.859421\pi\) | ||
0.904051 | − | 0.427425i | \(-0.140579\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.813607 | − | 3.91638i | 0.0755415 | − | 0.363627i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.10278 | − | 0.318888i | −0.285634 | − | 0.0293560i | ||||
\(119\) | −5.15667 | −0.472712 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −27.5089 | −2.50080 | ||||||||
\(122\) | 17.4600 | + | 1.79445i | 1.58075 | + | 0.162462i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.04888 | + | 1.04888i | 0.453402 | + | 0.0941918i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 10.4705i | − | 0.929110i | −0.885544 | − | 0.464555i | \(-0.846214\pi\) | ||
0.885544 | − | 0.464555i | \(-0.153786\pi\) | |||||||
\(128\) | −7.43375 | + | 8.52873i | −0.657057 | + | 0.753841i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4600i | 1.17600i | 0.808860 | + | 0.588002i | \(0.200085\pi\) | ||||
−0.808860 | + | 0.588002i | \(0.799915\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 20.4111 | 1.76987 | ||||||||
\(134\) | −0.578337 | + | 5.62721i | −0.0499607 | + | 0.486117i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.83276 | + | 1.21611i | 0.328657 | + | 0.104281i | ||||
\(137\) | 10.5783i | 0.903768i | 0.892077 | + | 0.451884i | \(0.149248\pi\) | ||||
−0.892077 | + | 0.451884i | \(0.850752\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 12.4705i | 1.05774i | 0.848704 | + | 0.528869i | \(0.177384\pi\) | ||||
−0.848704 | + | 0.528869i | \(0.822616\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.21611 | + | 11.8328i | −0.102054 | + | 0.992983i | ||||
\(143\) | 3.58890i | 0.300119i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 8.44082 | + | 0.867506i | 0.698567 | + | 0.0717953i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −15.3380 | − | 3.18639i | −1.26078 | − | 0.261920i | ||||
\(149\) | 2.00000i | 0.163846i | 0.996639 | + | 0.0819232i | \(0.0261062\pi\) | ||||
−0.996639 | + | 0.0819232i | \(0.973894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.6761 | 1.03157 | 0.515783 | − | 0.856719i | \(-0.327501\pi\) | ||||
0.515783 | + | 0.856719i | \(0.327501\pi\) | |||||||
\(152\) | −15.1708 | − | 4.81361i | −1.23051 | − | 0.390435i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3.25443 | + | 31.6655i | −0.262249 | + | 2.55168i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.32391 | 0.105660 | 0.0528298 | − | 0.998604i | \(-0.483176\pi\) | ||||
0.0528298 | + | 0.998604i | \(0.483176\pi\) | |||||||
\(158\) | −0.783887 | + | 7.62721i | −0.0623627 | + | 0.606788i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.4111 | −1.60862 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 15.2544 | 1.19482 | 0.597409 | − | 0.801936i | \(-0.296197\pi\) | ||||
0.597409 | + | 0.801936i | \(0.296197\pi\) | |||||||
\(164\) | 10.2892 | + | 2.13752i | 0.803449 | + | 0.166912i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.470539 | + | 4.57834i | −0.0365209 | + | 0.355348i | ||||
\(167\) | − | 10.7839i | − | 0.834482i | −0.908796 | − | 0.417241i | \(-0.862997\pi\) | ||
0.908796 | − | 0.417241i | \(-0.137003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6655 | −0.974271 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.2056 | + | 2.95112i | 1.08316 | + | 0.225021i | ||||
\(173\) | −13.6655 | −1.03897 | −0.519485 | − | 0.854479i | \(-0.673876\pi\) | ||||
−0.519485 | + | 0.854479i | \(0.673876\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 9.88666 | − | 22.7683i | 0.745235 | − | 1.71623i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.91638 | + | 18.6464i | −0.143639 | + | 1.39760i | ||||
\(179\) | − | 9.04888i | − | 0.676345i | −0.941084 | − | 0.338172i | \(-0.890191\pi\) | ||
0.941084 | − | 0.338172i | \(-0.109809\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.2544i | − | 1.72849i | −0.503073 | − | 0.864244i | \(-0.667797\pi\) | ||
0.503073 | − | 0.864244i | \(-0.332203\pi\) | |||||||
\(182\) | 2.95112 | + | 0.303302i | 0.218752 | + | 0.0224822i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.1708 | + | 4.81361i | 1.11841 | + | 0.354864i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.82220 | −0.645143 | ||||||||
\(188\) | −2.75971 | + | 13.2841i | −0.201272 | + | 0.968846i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.00000 | 0.578860 | 0.289430 | − | 0.957199i | \(-0.406534\pi\) | ||||
0.289430 | + | 0.957199i | \(0.406534\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 25.6655i | − | 1.84745i | −0.383062 | − | 0.923723i | \(-0.625131\pi\) | ||
0.383062 | − | 0.923723i | \(-0.374869\pi\) | |||||||
\(194\) | 6.81361 | + | 0.700269i | 0.489188 | + | 0.0502764i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 12.0559 | + | 2.50456i | 0.861139 | + | 0.178897i | ||||
\(197\) | 15.1567 | 1.07987 | 0.539934 | − | 0.841707i | \(-0.318449\pi\) | ||||
0.539934 | + | 0.841707i | \(0.318449\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.6761 | 1.46569 | 0.732845 | − | 0.680396i | \(-0.238192\pi\) | ||||
0.732845 | + | 0.680396i | \(0.238192\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.81361 | + | 0.289169i | 0.197965 | + | 0.0203458i | ||||
\(203\) | 7.25443 | 0.509161 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −3.47556 | − | 0.357201i | −0.242154 | − | 0.0248874i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.12193 | − | 0.921405i | −0.147129 | − | 0.0638879i | ||||
\(209\) | 34.9200 | 2.41546 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2.03831i | − | 0.140323i | −0.997536 | − | 0.0701616i | \(-0.977648\pi\) | ||
0.997536 | − | 0.0701616i | \(-0.0223515\pi\) | |||||||
\(212\) | −3.91638 | − | 0.813607i | −0.268978 | − | 0.0558787i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.03831 | − | 19.8328i | 0.139336 | − | 1.35574i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 9.35218i | 0.634867i | ||||||||
\(218\) | −10.2056 | − | 1.04888i | −0.691207 | − | 0.0710388i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.822200i | 0.0553072i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.21611i | 0.483227i | 0.970373 | + | 0.241613i | \(0.0776766\pi\) | ||||
−0.970373 | + | 0.241613i | \(0.922323\pi\) | |||||||
\(224\) | −17.8867 | − | 10.0539i | −1.19510 | − | 0.671754i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.7839 | − | 1.31386i | −0.850372 | − | 0.0873970i | ||||
\(227\) | 1.15667 | 0.0767712 | 0.0383856 | − | 0.999263i | \(-0.487778\pi\) | ||||
0.0383856 | + | 0.999263i | \(0.487778\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 14.0978i | − | 0.931606i | −0.884889 | − | 0.465803i | \(-0.845766\pi\) | ||
0.884889 | − | 0.465803i | \(-0.154234\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.39194 | − | 1.71083i | −0.353998 | − | 0.112322i | ||||
\(233\) | − | 14.5783i | − | 0.955059i | −0.878616 | − | 0.477529i | \(-0.841532\pi\) | ||
0.878616 | − | 0.477529i | \(-0.158468\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.897225 | + | 4.31889i | −0.0584044 | + | 0.281136i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.745574 | + | 7.25443i | −0.0483284 | + | 0.470235i | ||||
\(239\) | 19.2544 | 1.24547 | 0.622733 | − | 0.782435i | \(-0.286022\pi\) | ||||
0.622733 | + | 0.782435i | \(0.286022\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −13.6655 | −0.880274 | −0.440137 | − | 0.897931i | \(-0.645070\pi\) | ||||
−0.440137 | + | 0.897931i | \(0.645070\pi\) | |||||||
\(242\) | −3.97735 | + | 38.6995i | −0.255674 | + | 2.48770i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.04888 | − | 24.3033i | 0.323221 | − | 1.55586i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3.25443i | − | 0.207074i | ||||||
\(248\) | 2.20555 | − | 6.95112i | 0.140053 | − | 0.441397i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.14663i | 0.451091i | 0.974233 | + | 0.225546i | \(0.0724165\pi\) | ||||
−0.974233 | + | 0.225546i | \(0.927584\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −34.9200 | −2.19540 | ||||||||
\(254\) | −14.7300 | − | 1.51388i | −0.924242 | − | 0.0949890i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.9234 | + | 11.6909i | 0.682716 | + | 0.730684i | ||||
\(257\) | − | 7.73501i | − | 0.482497i | −0.970463 | − | 0.241248i | \(-0.922443\pi\) | ||
0.970463 | − | 0.241248i | \(-0.0775568\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 28.4111i | − | 1.76538i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 18.9355 | + | 1.94610i | 1.16984 | + | 0.120231i | ||||
\(263\) | − | 18.7839i | − | 1.15826i | −0.815234 | − | 0.579132i | \(-0.803392\pi\) | ||
0.815234 | − | 0.579132i | \(-0.196608\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.95112 | − | 28.7144i | 0.180945 | − | 1.76059i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 7.83276 | + | 1.62721i | 0.478462 | + | 0.0993979i | ||||
\(269\) | 8.50885i | 0.518794i | 0.965771 | + | 0.259397i | \(0.0835238\pi\) | ||||
−0.965771 | + | 0.259397i | \(0.916476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.9894 | 1.88247 | 0.941237 | − | 0.337746i | \(-0.109665\pi\) | ||||
0.941237 | + | 0.337746i | \(0.109665\pi\) | |||||||
\(272\) | 2.26499 | − | 5.21611i | 0.137335 | − | 0.316273i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 14.8816 | + | 1.52946i | 0.899033 | + | 0.0923981i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.51941 | −0.571966 | −0.285983 | − | 0.958235i | \(-0.592320\pi\) | ||||
−0.285983 | + | 0.958235i | \(0.592320\pi\) | |||||||
\(278\) | 17.5436 | + | 1.80304i | 1.05219 | + | 0.108139i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.6655 | −0.815217 | −0.407608 | − | 0.913157i | \(-0.633637\pi\) | ||||
−0.407608 | + | 0.913157i | \(0.633637\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.0000 | −1.18888 | −0.594438 | − | 0.804141i | \(-0.702626\pi\) | ||||
−0.594438 | + | 0.804141i | \(0.702626\pi\) | |||||||
\(284\) | 16.4705 | + | 3.42166i | 0.977347 | + | 0.203038i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.04888 | + | 0.518898i | 0.298546 | + | 0.0306831i | ||||
\(287\) | 19.0589i | 1.12501i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.9789 | 0.881110 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.44082 | − | 11.7491i | 0.142838 | − | 0.687567i | ||||
\(293\) | 4.31335 | 0.251989 | 0.125994 | − | 0.992031i | \(-0.459788\pi\) | ||||
0.125994 | + | 0.992031i | \(0.459788\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −6.70027 | + | 21.1169i | −0.389445 | + | 1.22740i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.81361 | + | 0.289169i | 0.162988 | + | 0.0167511i | ||||
\(299\) | 3.25443i | 0.188208i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 26.3133i | 1.51668i | ||||||||
\(302\) | 1.83276 | − | 17.8328i | 0.105464 | − | 1.02616i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.96526 | + | 20.6464i | −0.514193 | + | 1.18415i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.5678 | −1.45923 | −0.729615 | − | 0.683858i | \(-0.760301\pi\) | ||||
−0.729615 | + | 0.683858i | \(0.760301\pi\) | |||||||
\(308\) | 44.0766 | + | 9.15667i | 2.51150 | + | 0.521750i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 20.0766 | 1.13844 | 0.569221 | − | 0.822185i | \(-0.307245\pi\) | ||||
0.569221 | + | 0.822185i | \(0.307245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 7.15667i | − | 0.404519i | −0.979332 | − | 0.202260i | \(-0.935172\pi\) | ||
0.979332 | − | 0.202260i | \(-0.0648285\pi\) | |||||||
\(314\) | 0.191417 | − | 1.86248i | 0.0108023 | − | 0.105106i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.6167 | + | 2.20555i | 0.597233 | + | 0.124072i | ||||
\(317\) | 24.1744 | 1.35777 | 0.678884 | − | 0.734245i | \(-0.262464\pi\) | ||||
0.678884 | + | 0.734245i | \(0.262464\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.4111 | 0.694888 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.95112 | + | 28.7144i | −0.164460 | + | 1.60019i | ||||
\(323\) | 8.00000 | 0.445132 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.20555 | − | 21.4600i | 0.122154 | − | 1.18856i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.49472 | − | 14.1658i | 0.248179 | − | 0.782175i | ||||
\(329\) | −24.6066 | −1.35661 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 27.1950i | − | 1.49477i | −0.664390 | − | 0.747386i | \(-0.731309\pi\) | ||
0.664390 | − | 0.747386i | \(-0.268691\pi\) | |||||||
\(332\) | 6.37279 | + | 1.32391i | 0.349752 | + | 0.0726591i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −15.1708 | − | 1.55918i | −0.830110 | − | 0.0853146i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 22.8222i | 1.24320i | 0.783333 | + | 0.621602i | \(0.213518\pi\) | ||||
−0.783333 | + | 0.621602i | \(0.786482\pi\) | |||||||
\(338\) | −1.83124 | + | 17.8179i | −0.0996061 | + | 0.969166i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 16.0000i | 0.866449i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 3.05892i | − | 0.165166i | ||||||
\(344\) | 6.20555 | − | 19.5577i | 0.334581 | − | 1.05448i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.97582 | + | 19.2247i | −0.106221 | + | 1.03353i | ||||
\(347\) | −23.6655 | −1.27043 | −0.635216 | − | 0.772335i | \(-0.719089\pi\) | ||||
−0.635216 | + | 0.772335i | \(0.719089\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 34.9200i | 1.86922i | 0.355671 | + | 0.934611i | \(0.384252\pi\) | ||||
−0.355671 | + | 0.934611i | \(0.615748\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −30.6011 | − | 17.2005i | −1.63104 | − | 0.916791i | ||||
\(353\) | − | 15.9305i | − | 0.847896i | −0.905687 | − | 0.423948i | \(-0.860644\pi\) | ||
0.905687 | − | 0.423948i | \(-0.139356\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 25.9547 | + | 5.39194i | 1.37560 | + | 0.285772i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −12.7300 | − | 1.30833i | −0.672801 | − | 0.0691471i | ||||
\(359\) | 8.41110 | 0.443921 | 0.221960 | − | 0.975056i | \(-0.428754\pi\) | ||||
0.221960 | + | 0.975056i | \(0.428754\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −12.6655 | −0.666607 | ||||||||
\(362\) | −32.7144 | − | 3.36222i | −1.71943 | − | 0.176715i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.853372 | − | 4.10780i | 0.0447289 | − | 0.215307i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 24.4494i | − | 1.27625i | −0.769933 | − | 0.638124i | \(-0.779711\pi\) | ||
0.769933 | − | 0.638124i | \(-0.220289\pi\) | |||||||
\(368\) | 8.96526 | − | 20.6464i | 0.467346 | − | 1.07627i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 7.25443i | − | 0.376631i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.167237 | −0.00865920 | −0.00432960 | − | 0.999991i | \(-0.501378\pi\) | ||||
−0.00432960 | + | 0.999991i | \(0.501378\pi\) | |||||||
\(374\) | −1.27555 | + | 12.4111i | −0.0659572 | + | 0.641763i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.2892 | + | 5.80304i | 0.943192 | + | 0.299269i | ||||
\(377\) | − | 1.15667i | − | 0.0595718i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 7.72496i | − | 0.396805i | −0.980121 | − | 0.198402i | \(-0.936425\pi\) | ||
0.980121 | − | 0.198402i | \(-0.0635753\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.15667 | − | 11.2544i | 0.0591806 | − | 0.575827i | ||||
\(383\) | − | 1.62721i | − | 0.0831467i | −0.999135 | − | 0.0415734i | \(-0.986763\pi\) | ||
0.999135 | − | 0.0415734i | \(-0.0132370\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −36.1063 | − | 3.71083i | −1.83776 | − | 0.188876i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.97028 | − | 9.48416i | 0.100026 | − | 0.481485i | ||||
\(389\) | 12.3133i | 0.624312i | 0.950031 | + | 0.312156i | \(0.101051\pi\) | ||||
−0.950031 | + | 0.312156i | \(0.898949\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.00000 | −0.404577 | ||||||||
\(392\) | 5.26652 | − | 16.5982i | 0.265999 | − | 0.838337i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.19142 | − | 21.3225i | 0.110402 | − | 1.07421i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.0872 | 0.957959 | 0.478979 | − | 0.877826i | \(-0.341007\pi\) | ||||
0.478979 | + | 0.877826i | \(0.341007\pi\) | |||||||
\(398\) | 2.98944 | − | 29.0872i | 0.149847 | − | 1.45801i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 14.4111 | 0.719656 | 0.359828 | − | 0.933019i | \(-0.382835\pi\) | ||||
0.359828 | + | 0.933019i | \(0.382835\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.49115 | 0.0742794 | ||||||||
\(404\) | 0.813607 | − | 3.91638i | 0.0404784 | − | 0.194847i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.04888 | − | 10.2056i | 0.0520548 | − | 0.506493i | ||||
\(407\) | − | 48.6066i | − | 2.40934i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.31335 | 0.411069 | 0.205534 | − | 0.978650i | \(-0.434107\pi\) | ||||
0.205534 | + | 0.978650i | \(0.434107\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.00502 | + | 4.83779i | −0.0495139 | + | 0.238341i | ||||
\(413\) | −8.00000 | −0.393654 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.60303 | + | 2.85192i | −0.0785952 | + | 0.139827i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.04888 | − | 49.1255i | 0.246949 | − | 2.40281i | ||||
\(419\) | − | 7.36222i | − | 0.359668i | −0.983697 | − | 0.179834i | \(-0.942444\pi\) | ||
0.983697 | − | 0.179834i | \(-0.0575561\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 30.0978i | − | 1.46687i | −0.679757 | − | 0.733437i | \(-0.737915\pi\) | ||
0.679757 | − | 0.733437i | \(-0.262085\pi\) | |||||||
\(422\) | −2.86751 | − | 0.294708i | −0.139588 | − | 0.0143462i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.71083 | + | 5.39194i | −0.0830853 | + | 0.261856i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 45.0177 | 2.17856 | ||||||||
\(428\) | −27.6061 | − | 5.73501i | −1.33439 | − | 0.277212i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −8.41110 | −0.405148 | −0.202574 | − | 0.979267i | \(-0.564931\pi\) | ||||
−0.202574 | + | 0.979267i | \(0.564931\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.31335i | 0.207286i | 0.994615 | + | 0.103643i | \(0.0330500\pi\) | ||||
−0.994615 | + | 0.103643i | \(0.966950\pi\) | |||||||
\(434\) | 13.1567 | + | 1.35218i | 0.631541 | + | 0.0649066i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.95112 | + | 14.2056i | −0.141333 | + | 0.680322i | ||||
\(437\) | 31.6655 | 1.51477 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.83276 | −0.469292 | −0.234646 | − | 0.972081i | \(-0.575393\pi\) | ||||
−0.234646 | + | 0.972081i | \(0.575393\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.15667 | + | 0.118877i | 0.0550174 | + | 0.00565441i | ||||
\(443\) | −21.3522 | −1.01447 | −0.507236 | − | 0.861807i | \(-0.669333\pi\) | ||||
−0.507236 | + | 0.861807i | \(0.669333\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10.1517 | + | 1.04334i | 0.480695 | + | 0.0494034i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −16.7300 | + | 23.7094i | −0.790418 | + | 1.12016i | ||||
\(449\) | −20.3133 | −0.958646 | −0.479323 | − | 0.877639i | \(-0.659118\pi\) | ||||
−0.479323 | + | 0.877639i | \(0.659118\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 32.6066i | 1.53539i | ||||||||
\(452\) | −3.69670 | + | 17.7944i | −0.173878 | + | 0.836981i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0.167237 | − | 1.62721i | 0.00784882 | − | 0.0763689i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 3.35218i | − | 0.156808i | −0.996922 | − | 0.0784041i | \(-0.975018\pi\) | ||
0.996922 | − | 0.0784041i | \(-0.0249825\pi\) | |||||||
\(458\) | −19.8328 | − | 2.03831i | −0.926724 | − | 0.0952441i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 28.5089i | − | 1.32779i | −0.747826 | − | 0.663895i | \(-0.768902\pi\) | ||
0.747826 | − | 0.663895i | \(-0.231098\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 23.6272i | − | 1.09805i | −0.835806 | − | 0.549025i | \(-0.814999\pi\) | ||
0.835806 | − | 0.549025i | \(-0.185001\pi\) | |||||||
\(464\) | −3.18639 | + | 7.33804i | −0.147925 | + | 0.340660i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.5089 | − | 2.10780i | −0.950054 | − | 0.0976419i | ||||
\(467\) | −29.5678 | −1.36823 | −0.684117 | − | 0.729373i | \(-0.739812\pi\) | ||||
−0.684117 | + | 0.729373i | \(0.739812\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.5089i | 0.669957i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 5.94610 | + | 1.88666i | 0.273691 | + | 0.0868407i | ||||
\(473\) | 45.0177i | 2.06992i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 10.0978 | + | 2.09775i | 0.462830 | + | 0.0961503i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.78389 | − | 27.0872i | 0.127332 | − | 1.23894i | ||||
\(479\) | −22.0978 | −1.00967 | −0.504836 | − | 0.863215i | \(-0.668447\pi\) | ||||
−0.504836 | + | 0.863215i | \(0.668447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.52998 | −0.206549 | ||||||||
\(482\) | −1.97582 | + | 19.2247i | −0.0899961 | + | 0.875661i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 53.8676 | + | 11.1907i | 2.44853 | + | 0.508668i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.03831i | 0.182993i | 0.995805 | + | 0.0914967i | \(0.0291651\pi\) | ||||
−0.995805 | + | 0.0914967i | \(0.970835\pi\) | |||||||
\(488\) | −33.4600 | − | 10.6167i | −1.51466 | − | 0.480593i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 18.2056i | − | 0.821605i | −0.911724 | − | 0.410802i | \(-0.865249\pi\) | ||
0.911724 | − | 0.410802i | \(-0.134751\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.84333 | 0.128057 | ||||||||
\(494\) | −4.57834 | − | 0.470539i | −0.205989 | − | 0.0211705i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.45998 | − | 4.10780i | −0.424765 | − | 0.184446i | ||||
\(497\) | 30.5089i | 1.36851i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 0.0594386i | − | 0.00266084i | −0.999999 | − | 0.00133042i | \(-0.999577\pi\) | ||
0.999999 | − | 0.00133042i | \(-0.000423486\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 10.0539 | + | 1.03329i | 0.448727 | + | 0.0461180i | ||||
\(503\) | 2.03831i | 0.0908839i | 0.998967 | + | 0.0454419i | \(0.0144696\pi\) | ||||
−0.998967 | + | 0.0454419i | \(0.985530\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.04888 | + | 49.1255i | −0.224450 | + | 2.18389i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −4.25945 | + | 20.5033i | −0.188983 | + | 0.909687i | ||||
\(509\) | − | 40.7044i | − | 1.80419i | −0.431539 | − | 0.902094i | \(-0.642029\pi\) | ||
0.431539 | − | 0.902094i | \(-0.357971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.7633 | 0.962751 | ||||||||
\(512\) | 18.0262 | − | 13.6768i | 0.796654 | − | 0.604436i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −10.8816 | − | 1.11836i | −0.479969 | − | 0.0493288i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −42.0978 | −1.85146 | ||||||||
\(518\) | −39.9688 | − | 4.10780i | −1.75613 | − | 0.180486i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −10.0000 | −0.438108 | −0.219054 | − | 0.975713i | \(-0.570297\pi\) | ||||
−0.219054 | + | 0.975713i | \(0.570297\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.3311 | 1.54492 | 0.772460 | − | 0.635064i | \(-0.219026\pi\) | ||||
0.772460 | + | 0.635064i | \(0.219026\pi\) | |||||||
\(524\) | 5.47556 | − | 26.3572i | 0.239201 | − | 1.15142i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −26.4252 | − | 2.71585i | −1.15219 | − | 0.118417i | ||||
\(527\) | 3.66553i | 0.159673i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.66553 | −0.376762 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −39.9688 | − | 8.30330i | −1.73287 | − | 0.359994i | ||||
\(533\) | 3.03883 | 0.131626 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.42166 | − | 10.7839i | 0.147793 | − | 0.465793i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 11.9703 | + | 1.23025i | 0.516075 | + | 0.0530397i | ||||
\(539\) | 38.2056i | 1.64563i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.05892i | 0.131513i | 0.997836 | + | 0.0657567i | \(0.0209461\pi\) | ||||
−0.997836 | + | 0.0657567i | \(0.979054\pi\) | |||||||
\(542\) | 4.48059 | − | 43.5960i | 0.192458 | − | 1.87261i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −7.01056 | − | 3.94056i | −0.300575 | − | 0.168950i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0766 | 1.37150 | 0.685749 | − | 0.727838i | \(-0.259475\pi\) | ||||
0.685749 | + | 0.727838i | \(0.259475\pi\) | |||||||
\(548\) | 4.30330 | − | 20.7144i | 0.183828 | − | 0.884875i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.2544 | −0.479455 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 19.6655i | 0.836263i | ||||||||
\(554\) | −1.37636 | + | 13.3919i | −0.0584758 | + | 0.568969i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.07306 | − | 24.4197i | 0.215145 | − | 1.03563i | ||||
\(557\) | −33.6655 | −1.42645 | −0.713227 | − | 0.700933i | \(-0.752767\pi\) | ||||
−0.713227 | + | 0.700933i | \(0.752767\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 4.19550 | 0.177451 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.97582 | + | 19.2247i | −0.0833449 | + | 0.810945i | ||||
\(563\) | 5.35218 | 0.225567 | 0.112784 | − | 0.993620i | \(-0.464023\pi\) | ||||
0.112784 | + | 0.993620i | \(0.464023\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.89169 | + | 28.1361i | −0.121547 | + | 1.18265i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.19499 | − | 22.6761i | 0.301895 | − | 0.951468i | ||||
\(569\) | 5.58890 | 0.234299 | 0.117149 | − | 0.993114i | \(-0.462624\pi\) | ||||
0.117149 | + | 0.993114i | \(0.462624\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 10.3728i | − | 0.434088i | −0.976162 | − | 0.217044i | \(-0.930359\pi\) | ||
0.976162 | − | 0.217044i | \(-0.0696414\pi\) | |||||||
\(572\) | 1.45998 | − | 7.02775i | 0.0610447 | − | 0.293845i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 26.8122 | + | 2.75562i | 1.11912 | + | 0.115017i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 21.6655i | 0.901948i | 0.892537 | + | 0.450974i | \(0.148923\pi\) | ||||
−0.892537 | + | 0.450974i | \(0.851077\pi\) | |||||||
\(578\) | 2.16571 | − | 21.0723i | 0.0900816 | − | 0.876493i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.8045i | 0.489733i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 12.4111i | − | 0.514015i | ||||||
\(584\) | −16.1758 | − | 5.13249i | −0.669361 | − | 0.212384i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.623642 | − | 6.06803i | 0.0257624 | − | 0.250668i | ||||
\(587\) | 1.90225 | 0.0785142 | 0.0392571 | − | 0.999229i | \(-0.487501\pi\) | ||||
0.0392571 | + | 0.999229i | \(0.487501\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 14.5089i | − | 0.597827i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 28.7386 | + | 12.4791i | 1.18115 | + | 0.512889i | ||||
\(593\) | − | 2.57834i | − | 0.105880i | −0.998598 | − | 0.0529398i | \(-0.983141\pi\) | ||
0.998598 | − | 0.0529398i | \(-0.0168591\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.813607 | − | 3.91638i | 0.0333266 | − | 0.160421i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.57834 | + | 0.470539i | 0.187222 | + | 0.0192418i | ||||
\(599\) | 26.7244 | 1.09193 | 0.545966 | − | 0.837808i | \(-0.316163\pi\) | ||||
0.545966 | + | 0.837808i | \(0.316163\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 33.3311 | 1.35960 | 0.679801 | − | 0.733397i | \(-0.262066\pi\) | ||||
0.679801 | + | 0.733397i | \(0.262066\pi\) | |||||||
\(602\) | 37.0177 | + | 3.80450i | 1.50873 | + | 0.155060i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −24.8222 | − | 5.15667i | −1.01000 | − | 0.209822i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21.9406i | − | 0.890540i | −0.895396 | − | 0.445270i | \(-0.853108\pi\) | ||
0.895396 | − | 0.445270i | \(-0.146892\pi\) | |||||||
\(608\) | 27.7491 | + | 15.5975i | 1.12538 | + | 0.632562i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.92337i | 0.158723i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.42166 | −0.138200 | −0.0690998 | − | 0.997610i | \(-0.522013\pi\) | ||||
−0.0690998 | + | 0.997610i | \(0.522013\pi\) | |||||||
\(614\) | −3.69670 | + | 35.9688i | −0.149187 | + | 1.45158i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 19.2544 | − | 60.6832i | 0.775783 | − | 2.44500i | ||||
\(617\) | − | 19.7350i | − | 0.794502i | −0.917710 | − | 0.397251i | \(-0.869964\pi\) | ||
0.917710 | − | 0.397251i | \(-0.130036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.4705i | 0.822780i | 0.911459 | + | 0.411390i | \(0.134957\pi\) | ||||
−0.911459 | + | 0.411390i | \(0.865043\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.90276 | − | 28.2439i | 0.116390 | − | 1.13248i | ||||
\(623\) | 48.0766i | 1.92615i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −10.0680 | − | 1.03474i | −0.402400 | − | 0.0413566i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.59247 | − | 0.538571i | −0.103451 | − | 0.0214913i | ||||
\(629\) | − | 11.1355i | − | 0.444003i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.08719 | 0.0432803 | 0.0216402 | − | 0.999766i | \(-0.493111\pi\) | ||||
0.0216402 | + | 0.999766i | \(0.493111\pi\) | |||||||
\(632\) | 4.63778 | − | 14.6167i | 0.184481 | − | 0.581419i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.49523 | − | 34.0086i | 0.138814 | − | 1.35065i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.56063 | 0.141077 | ||||||||
\(638\) | 1.79445 | − | 17.4600i | 0.0710430 | − | 0.691247i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27.9789 | 1.10510 | 0.552550 | − | 0.833480i | \(-0.313655\pi\) | ||||
0.552550 | + | 0.833480i | \(0.313655\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −4.94108 | −0.194857 | −0.0974285 | − | 0.995243i | \(-0.531062\pi\) | ||||
−0.0974285 | + | 0.995243i | \(0.531062\pi\) | |||||||
\(644\) | 39.9688 | + | 8.30330i | 1.57499 | + | 0.327196i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.15667 | − | 11.2544i | 0.0455087 | − | 0.442799i | ||||
\(647\) | 49.3694i | 1.94091i | 0.241282 | + | 0.970455i | \(0.422432\pi\) | ||||
−0.241282 | + | 0.970455i | \(0.577568\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.6867 | −0.537248 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −29.8711 | − | 6.20555i | −1.16984 | − | 0.243028i | ||||
\(653\) | 40.1744 | 1.57214 | 0.786072 | − | 0.618134i | \(-0.212111\pi\) | ||||
0.786072 | + | 0.618134i | \(0.212111\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −19.2786 | − | 8.37133i | −0.752703 | − | 0.326846i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.55773 | + | 34.6167i | −0.138695 | + | 1.34950i | ||||
\(659\) | 21.1255i | 0.822933i | 0.911425 | + | 0.411466i | \(0.134983\pi\) | ||||
−0.911425 | + | 0.411466i | \(0.865017\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.9200i | 0.424737i | 0.977190 | + | 0.212368i | \(0.0681177\pi\) | ||||
−0.977190 | + | 0.212368i | \(0.931882\pi\) | |||||||
\(662\) | −38.2580 | − | 3.93197i | −1.48694 | − | 0.152820i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.78389 | − | 8.77384i | 0.108036 | − | 0.340491i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.2544 | 0.435773 | ||||||||
\(668\) | −4.38692 | + | 21.1169i | −0.169735 | + | 0.817038i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 77.0177 | 2.97324 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.0000i | 0.693849i | 0.937893 | + | 0.346925i | \(0.112774\pi\) | ||||
−0.937893 | + | 0.346925i | \(0.887226\pi\) | |||||||
\(674\) | 32.1063 | + | 3.29973i | 1.23669 | + | 0.127101i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 24.8015 | + | 5.15238i | 0.953904 | + | 0.198168i | ||||
\(677\) | −30.4877 | −1.17174 | −0.585869 | − | 0.810406i | \(-0.699247\pi\) | ||||
−0.585869 | + | 0.810406i | \(0.699247\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.5678 | 0.674189 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 22.5089 | + | 2.31335i | 0.861908 | + | 0.0885827i | ||||
\(683\) | −35.2544 | −1.34897 | −0.674487 | − | 0.738287i | \(-0.735635\pi\) | ||||
−0.674487 | + | 0.738287i | \(0.735635\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.30330 | − | 0.442272i | −0.164301 | − | 0.0168860i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −26.6167 | − | 11.5577i | −1.01475 | − | 0.440634i | ||||
\(689\) | −1.15667 | −0.0440658 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.1361i | 1.07035i | 0.844742 | + | 0.535173i | \(0.179754\pi\) | ||||
−0.844742 | + | 0.535173i | \(0.820246\pi\) | |||||||
\(692\) | 26.7597 | + | 5.55918i | 1.01725 | + | 0.211328i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.42166 | + | 33.2927i | −0.129885 | + | 1.26378i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.47002i | 0.282947i | ||||||||
\(698\) | 49.1255 | + | 5.04888i | 1.85943 | + | 0.191103i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 34.8222i | − | 1.31522i | −0.753360 | − | 0.657608i | \(-0.771568\pi\) | ||
0.753360 | − | 0.657608i | \(-0.228432\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 44.0766i | 1.66238i | ||||||||
\(704\) | −28.6222 | + | 40.5628i | −1.07874 | + | 1.52877i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −22.4111 | − | 2.30330i | −0.843453 | − | 0.0866859i | ||||
\(707\) | 7.25443 | 0.272831 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 7.58890i | − | 0.285007i | −0.989794 | − | 0.142504i | \(-0.954485\pi\) | ||
0.989794 | − | 0.142504i | \(-0.0455152\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 11.3380 | − | 35.7336i | 0.424911 | − | 1.33917i | ||||
\(713\) | 14.5089i | 0.543361i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −3.68111 | + | 17.7194i | −0.137570 | + | 0.662206i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.21611 | − | 11.8328i | 0.0453849 | − | 0.441595i | ||||
\(719\) | −3.66553 | −0.136701 | −0.0683505 | − | 0.997661i | \(-0.521774\pi\) | ||||
−0.0683505 | + | 0.997661i | \(0.521774\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.96117 | −0.333731 | ||||||||
\(722\) | −1.83124 | + | 17.8179i | −0.0681515 | + | 0.663114i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −9.45998 | + | 45.5366i | −0.351577 | + | 1.69235i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 36.1149i | − | 1.33943i | −0.742619 | − | 0.669714i | \(-0.766416\pi\) | ||
0.742619 | − | 0.669714i | \(-0.233584\pi\) | |||||||
\(728\) | −5.65548 | − | 1.79445i | −0.209606 | − | 0.0665067i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.3133i | 0.381453i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.0071 | 1.25608 | 0.628041 | − | 0.778180i | \(-0.283857\pi\) | ||||
0.628041 | + | 0.778180i | \(0.283857\pi\) | |||||||
\(734\) | −34.3955 | − | 3.53500i | −1.26956 | − | 0.130479i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −27.7491 | − | 15.5975i | −1.02285 | − | 0.574931i | ||||
\(737\) | 24.8222i | 0.914338i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 52.0172i | − | 1.91348i | −0.290939 | − | 0.956742i | \(-0.593968\pi\) | ||
0.290939 | − | 0.956742i | \(-0.406032\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −10.2056 | − | 1.04888i | −0.374658 | − | 0.0385054i | ||||
\(743\) | − | 23.3139i | − | 0.855303i | −0.903944 | − | 0.427651i | \(-0.859341\pi\) | ||
0.903944 | − | 0.427651i | \(-0.140659\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −0.0241798 | + | 0.235269i | −0.000885286 | + | 0.00861383i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 17.2756 | + | 3.58890i | 0.631657 | + | 0.131223i | ||||
\(749\) | − | 51.1355i | − | 1.86845i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11.1083 | 0.405348 | 0.202674 | − | 0.979246i | \(-0.435037\pi\) | ||||
0.202674 | + | 0.979246i | \(0.435037\pi\) | |||||||
\(752\) | 10.8081 | − | 24.8902i | 0.394130 | − | 0.907653i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −1.62721 | − | 0.167237i | −0.0592596 | − | 0.00609041i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.3239 | −0.484266 | −0.242133 | − | 0.970243i | \(-0.577847\pi\) | ||||
−0.242133 | + | 0.970243i | \(0.577847\pi\) | |||||||
\(758\) | −10.8675 | − | 1.11691i | −0.394726 | − | 0.0405679i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 17.1355 | 0.621163 | 0.310582 | − | 0.950547i | \(-0.399476\pi\) | ||||
0.310582 | + | 0.950547i | \(0.399476\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −26.3133 | −0.952607 | ||||||||
\(764\) | −15.6655 | − | 3.25443i | −0.566759 | − | 0.117741i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.28917 | − | 0.235269i | −0.0827110 | − | 0.00850063i | ||||
\(767\) | 1.27555i | 0.0460575i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5.47002 | −0.197254 | −0.0986270 | − | 0.995124i | \(-0.531445\pi\) | ||||
−0.0986270 | + | 0.995124i | \(0.531445\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.4408 | + | 50.2580i | −0.375773 | + | 1.80882i | ||||
\(773\) | 3.15667 | 0.113538 | 0.0567688 | − | 0.998387i | \(-0.481920\pi\) | ||||
0.0567688 | + | 0.998387i | \(0.481920\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −13.0575 | − | 4.14306i | −0.468736 | − | 0.148727i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 17.3225 | + | 1.78032i | 0.621040 | + | 0.0638274i | ||||
\(779\) | − | 29.5678i | − | 1.05938i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 52.1955i | 1.86770i | ||||||||
\(782\) | −1.15667 | + | 11.2544i | −0.0413626 | + | 0.402457i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −22.5890 | − | 9.80879i | −0.806749 | − | 0.350314i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −31.1355 | −1.10986 | −0.554931 | − | 0.831896i | \(-0.687255\pi\) | ||||
−0.554931 | + | 0.831896i | \(0.687255\pi\) | |||||||
\(788\) | −29.6797 | − | 6.16578i | −1.05729 | − | 0.219647i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −32.9612 | −1.17196 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 7.17780i | − | 0.254891i | ||||||
\(794\) | 2.75971 | − | 26.8519i | 0.0979383 | − | 0.952939i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −40.4877 | − | 8.41110i | −1.43505 | − | 0.298124i | ||||
\(797\) | −10.0000 | −0.354218 | −0.177109 | − | 0.984191i | \(-0.556675\pi\) | ||||
−0.177109 | + | 0.984191i | \(0.556675\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.64440 | −0.341194 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.08362 | − | 20.2736i | 0.0735751 | − | 0.715885i | ||||
\(803\) | 37.2333 | 1.31393 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.215597 | − | 2.09775i | 0.00759406 | − | 0.0738902i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.39194 | − | 1.71083i | −0.189688 | − | 0.0601868i | ||||
\(809\) | 29.0388 | 1.02095 | 0.510475 | − | 0.859892i | \(-0.329469\pi\) | ||||
0.510475 | + | 0.859892i | \(0.329469\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.58838i | 0.0908904i | 0.998967 | + | 0.0454452i | \(0.0144706\pi\) | ||||
−0.998967 | + | 0.0454452i | \(0.985529\pi\) | |||||||
\(812\) | −14.2056 | − | 2.95112i | −0.498517 | − | 0.103564i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −68.3799 | − | 7.02775i | −2.39672 | − | 0.246323i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 40.8222i | − | 1.42819i | ||||||
\(818\) | 1.20198 | − | 11.6952i | 0.0420262 | − | 0.408915i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.1955i | 1.33303i | 0.745491 | + | 0.666516i | \(0.232215\pi\) | ||||
−0.745491 | + | 0.666516i | \(0.767785\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18.3517i | 0.639699i | 0.947468 | + | 0.319849i | \(0.103632\pi\) | ||||
−0.947468 | + | 0.319849i | \(0.896368\pi\) | |||||||
\(824\) | 6.66050 | + | 2.11334i | 0.232030 | + | 0.0736216i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.15667 | + | 11.2544i | −0.0402458 | + | 0.391592i | ||||
\(827\) | 20.0000 | 0.695468 | 0.347734 | − | 0.937593i | \(-0.386951\pi\) | ||||
0.347734 | + | 0.937593i | \(0.386951\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 24.7456i | 0.859449i | 0.902960 | + | 0.429725i | \(0.141389\pi\) | ||||
−0.902960 | + | 0.429725i | \(0.858611\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.78032 | + | 2.66750i | 0.131059 | + | 0.0924788i | ||||
\(833\) | 8.75272i | 0.303264i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −68.3799 | − | 14.2056i | −2.36497 | − | 0.491309i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10.3572 | − | 1.06446i | −0.357784 | − | 0.0367712i | ||||
\(839\) | −53.4288 | −1.84457 | −0.922284 | − | 0.386514i | \(-0.873679\pi\) | ||||
−0.922284 | + | 0.386514i | \(0.873679\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.0000 | 0.862069 | ||||||||
\(842\) | −42.3416 | − | 4.35166i | −1.45919 | − | 0.149968i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −0.829192 | + | 3.99141i | −0.0285420 | + | 0.137390i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 99.7805i | 3.42850i | ||||||||
\(848\) | 7.33804 | + | 3.18639i | 0.251989 | + | 0.109421i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 44.0766i | − | 1.51093i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −29.0661 | −0.995203 | −0.497602 | − | 0.867406i | \(-0.665786\pi\) | ||||
−0.497602 | + | 0.867406i | \(0.665786\pi\) | |||||||
\(854\) | 6.50885 | − | 63.3311i | 0.222728 | − | 2.16714i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.0594 | + | 38.0071i | −0.412183 | + | 1.29906i | ||||
\(857\) | 10.2439i | 0.349924i | 0.984575 | + | 0.174962i | \(0.0559802\pi\) | ||||
−0.984575 | + | 0.174962i | \(0.944020\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10.9794i | 0.374612i | 0.982302 | + | 0.187306i | \(0.0599756\pi\) | ||||
−0.982302 | + | 0.187306i | \(0.940024\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.21611 | + | 11.8328i | −0.0414210 | + | 0.403026i | ||||
\(863\) | 38.8605i | 1.32283i | 0.750021 | + | 0.661414i | \(0.230043\pi\) | ||||
−0.750021 | + | 0.661414i | \(0.769957\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 6.06803 | + | 0.623642i | 0.206200 | + | 0.0211922i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 3.80450 | − | 18.3133i | 0.129133 | − | 0.621596i | ||||
\(869\) | 33.6444i | 1.14131i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.31335 | 0.0783848 | ||||||||
\(872\) | 19.5577 | + | 6.20555i | 0.662308 | + | 0.210146i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.57834 | − | 44.5472i | 0.154865 | − | 1.50683i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 22.3416 | 0.754423 | 0.377211 | − | 0.926127i | \(-0.376883\pi\) | ||||
0.377211 | + | 0.926127i | \(0.376883\pi\) | |||||||
\(878\) | −1.42166 | + | 13.8328i | −0.0479788 | + | 0.466833i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.88112 | −0.332903 | −0.166452 | − | 0.986050i | \(-0.553231\pi\) | ||||
−0.166452 | + | 0.986050i | \(0.553231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 10.6277 | 0.357652 | 0.178826 | − | 0.983881i | \(-0.442770\pi\) | ||||
0.178826 | + | 0.983881i | \(0.442770\pi\) | |||||||
\(884\) | 0.334474 | − | 1.61003i | 0.0112496 | − | 0.0541510i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.08719 | + | 30.0383i | −0.103716 | + | 1.00916i | ||||
\(887\) | − | 11.6061i | − | 0.389694i | −0.980834 | − | 0.194847i | \(-0.937579\pi\) | ||
0.980834 | − | 0.194847i | \(-0.0624211\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −37.9789 | −1.27377 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 2.93554 | − | 14.1305i | 0.0982891 | − | 0.473125i | ||||
\(893\) | 38.1744 | 1.27746 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 30.9355 | + | 26.9638i | 1.03348 | + | 0.900797i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −2.93699 | + | 28.5769i | −0.0980086 | + | 0.953623i | ||||
\(899\) | − | 5.15667i | − | 0.171985i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 2.84333i | − | 0.0947249i | ||||||
\(902\) | 45.8711 | + | 4.71440i | 1.52734 | + | 0.156972i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 24.4988 | + | 7.77332i | 0.814818 | + | 0.258537i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −0.195504 | −0.00649159 | −0.00324580 | − | 0.999995i | \(-0.501033\pi\) | ||||
−0.00324580 | + | 0.999995i | \(0.501033\pi\) | |||||||
\(908\) | −2.26499 | − | 0.470539i | −0.0751663 | − | 0.0156154i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.88112 | 0.261113 | 0.130557 | − | 0.991441i | \(-0.458324\pi\) | ||||
0.130557 | + | 0.991441i | \(0.458324\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.1955i | 0.668374i | ||||||||
\(914\) | −4.71585 | − | 0.484672i | −0.155987 | − | 0.0160315i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5.73501 | + | 27.6061i | −0.189490 | + | 0.912131i | ||||
\(917\) | 48.8222 | 1.61225 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.75614 | −0.321825 | −0.160913 | − | 0.986969i | \(-0.551444\pi\) | ||||
−0.160913 | + | 0.986969i | \(0.551444\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −40.1063 | − | 4.12193i | −1.32083 | − | 0.135749i | ||||
\(923\) | 4.86445 | 0.160115 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −33.2388 | − | 3.41612i | −1.09230 | − | 0.112261i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 9.86248 | + | 5.54359i | 0.323752 | + | 0.181977i | ||||
\(929\) | 6.82220 | 0.223829 | 0.111915 | − | 0.993718i | \(-0.464302\pi\) | ||||
0.111915 | + | 0.993718i | \(0.464302\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 34.6449i | − | 1.13544i | ||||||
\(932\) | −5.93051 | + | 28.5472i | −0.194260 | + | 0.935093i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −4.27504 | + | 41.5960i | −0.139883 | + | 1.36106i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 57.5266i | 1.87931i | 0.342123 | + | 0.939655i | \(0.388854\pi\) | ||||
−0.342123 | + | 0.939655i | \(0.611146\pi\) | |||||||
\(938\) | 20.4111 | + | 2.09775i | 0.666446 | + | 0.0684940i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 0.508852i | 0.0165881i | 0.999966 | + | 0.00829405i | \(0.00264011\pi\) | ||||
−0.999966 | + | 0.00829405i | \(0.997360\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 29.5678i | 0.962859i | ||||||||
\(944\) | 3.51388 | − | 8.09221i | 0.114367 | − | 0.263379i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 63.3311 | + | 6.50885i | 2.05907 | + | 0.211621i | ||||
\(947\) | 1.68665 | 0.0548088 | 0.0274044 | − | 0.999624i | \(-0.491276\pi\) | ||||
0.0274044 | + | 0.999624i | \(0.491276\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 3.47002i | − | 0.112642i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.41110 | − | 13.9022i | 0.142965 | − | 0.450574i | ||||
\(953\) | 9.22616i | 0.298865i | 0.988772 | + | 0.149432i | \(0.0477446\pi\) | ||||
−0.988772 | + | 0.149432i | \(0.952255\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −37.7038 | − | 7.83276i | −1.21943 | − | 0.253330i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −3.19499 | + | 31.0872i | −0.103225 | + | 1.00438i | ||||
\(959\) | 38.3699 | 1.23903 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.3522 | −0.785554 | ||||||||
\(962\) | −0.654963 | + | 6.37279i | −0.0211169 | + | 0.205467i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 26.7597 | + | 5.55918i | 0.861872 | + | 0.179049i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.2338i | 0.393413i | 0.980462 | + | 0.196707i | \(0.0630246\pi\) | ||||
−0.980462 | + | 0.196707i | \(0.936975\pi\) | |||||||
\(968\) | 23.5315 | − | 74.1631i | 0.756331 | − | 2.38369i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 33.2444i | − | 1.06686i | −0.845843 | − | 0.533431i | \(-0.820902\pi\) | ||
0.845843 | − | 0.533431i | \(-0.179098\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 45.2333 | 1.45011 | ||||||||
\(974\) | 5.68111 | + | 0.583877i | 0.182035 | + | 0.0187086i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −19.7733 | + | 45.5366i | −0.632929 | + | 1.45759i | ||||
\(977\) | − | 7.93051i | − | 0.253720i | −0.991921 | − | 0.126860i | \(-0.959510\pi\) | ||
0.991921 | − | 0.126860i | \(-0.0404898\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 82.2510i | 2.62875i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −25.6116 | − | 2.63224i | −0.817300 | − | 0.0839980i | ||||
\(983\) | 41.8993i | 1.33638i | 0.743990 | + | 0.668191i | \(0.232931\pi\) | ||||
−0.743990 | + | 0.668191i | \(0.767069\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0.411100 | − | 4.00000i | 0.0130921 | − | 0.127386i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.32391 | + | 6.37279i | −0.0421192 | + | 0.202745i | ||||
\(989\) | 40.8222i | 1.29807i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −35.1849 | −1.11769 | −0.558843 | − | 0.829273i | \(-0.688755\pi\) | ||||
−0.558843 | + | 0.829273i | \(0.688755\pi\) | |||||||
\(992\) | −7.14663 | + | 12.7144i | −0.226906 | + | 0.403683i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 42.9200 | + | 4.41110i | 1.36134 | + | 0.139912i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −8.04836 | −0.254894 | −0.127447 | − | 0.991845i | \(-0.540678\pi\) | ||||
−0.127447 | + | 0.991845i | \(0.540678\pi\) | |||||||
\(998\) | −0.0836184 | − | 0.00859389i | −0.00264690 | − | 0.000272035i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))